Properties

Modulus $5850$
Structure \(C_{2}\times C_{12}\times C_{60}\)
Order $1440$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(5850)
 
pari: g = idealstar(,5850,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1440
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{12}\times C_{60}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{5850}(3251,\cdot)$, $\chi_{5850}(3277,\cdot)$, $\chi_{5850}(2251,\cdot)$

First 32 of 1440 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character Orbit Order Primitive \(-1\) \(1\) \(7\) \(11\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{5850}(1,\cdot)\) 5850.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{5850}(7,\cdot)\) 5850.ed 12 no \(1\) \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(i\)
\(\chi_{5850}(11,\cdot)\) 5850.gz 60 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5850}(17,\cdot)\) 5850.hg 60 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{5850}(19,\cdot)\) 5850.gy 60 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{5850}(23,\cdot)\) 5850.hf 60 no \(1\) \(1\) \(i\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{1}{5}\right)\) \(i\)
\(\chi_{5850}(29,\cdot)\) 5850.fs 30 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5850}(31,\cdot)\) 5850.hb 60 no \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5850}(37,\cdot)\) 5850.ga 60 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{5850}(41,\cdot)\) 5850.gu 60 no \(1\) \(1\) \(i\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(-1\)
\(\chi_{5850}(43,\cdot)\) 5850.dq 12 no \(-1\) \(1\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(i\)
\(\chi_{5850}(47,\cdot)\) 5850.gb 60 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{5850}(49,\cdot)\) 5850.ca 6 no \(1\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(-1\)
\(\chi_{5850}(53,\cdot)\) 5850.er 20 no \(1\) \(1\) \(-i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(i\)
\(\chi_{5850}(59,\cdot)\) 5850.gr 60 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{5850}(61,\cdot)\) 5850.eh 15 no \(1\) \(1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\)
\(\chi_{5850}(67,\cdot)\) 5850.fw 60 no \(1\) \(1\) \(-1\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{7}{20}\right)\) \(i\)
\(\chi_{5850}(71,\cdot)\) 5850.gx 60 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5850}(73,\cdot)\) 5850.ej 20 no \(1\) \(1\) \(-1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(-i\)
\(\chi_{5850}(77,\cdot)\) 5850.hc 60 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{5850}(79,\cdot)\) 5850.fp 30 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{5850}(83,\cdot)\) 5850.gb 60 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{5850}(89,\cdot)\) 5850.gp 60 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{5850}(97,\cdot)\) 5850.fw 60 no \(1\) \(1\) \(-1\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{3}{20}\right)\) \(i\)
\(\chi_{5850}(101,\cdot)\) 5850.bx 6 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{5850}(103,\cdot)\) 5850.gg 60 no \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{5850}(107,\cdot)\) 5850.ds 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{5850}(109,\cdot)\) 5850.em 20 no \(-1\) \(1\) \(-i\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(1\)
\(\chi_{5850}(113,\cdot)\) 5850.hi 60 no \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{5850}(119,\cdot)\) 5850.gr 60 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{5850}(121,\cdot)\) 5850.fr 30 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{5850}(127,\cdot)\) 5850.gk 60 no \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{5}{12}\right)\)
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